Abstract We use tsunami records from five early Pacific tide gauges in the United States and Australia to estimate the size of the 1868 and 1877 Chile‐Peru earthquakes—two of the largest documented in South America since colonial times. To interpret these records, we derive empirical relationships between moment magnitude (Mw) and maximum tsunami amplitude (MTA) for the five remote tide gauge locations using synthetic Mw 8–9 Chile‐Peru earthquakes and validate them with recent events. We infer Mw 8.8–9.1 for the 1868 earthquake and Mw 8.8–8.9 for the 1877 earthquake, clarifying a long‐standing debate and providing key insights for hazard models for this region. Our results confirm that MTA is predominantly controlled by Mw, but is also influenced by rupture strike, rupture length, and slip size; given Mw, greater slip over a shorter rupture increases MTA. These findings offer globally relevant insights into how source parameters influence far‐field tsunami amplitudes.

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